Single-hole spectral functions in 1D quantum magnets with different ground states

Thanks to improved methods for numerical analytic continuation with constraints, spectral functions with sharp features can now be extracted from imaginary-time correlation functions computed by quantum Monte Carlo (QMC) simulations. Here we test these new approaches on various one-dimensional $S=1\mathrm{/}2$ spin systems with a single ejected fermion, i.e., extracting the single-hole spectral function $A(k,\omega )$. We compute the Green’s function $G(r,\tau )$ via a canonical transformation of the fermionic Hamiltonian, implementing it for stochastic series expansion QMC simulations. Our calculations of $A(k,\omega )$ focus on the different characteristics of systems with spin-charge separation and those in which a spin polaron forms instead due to effectively attractive interactions between the spin and the charge. Spin-charge separation is well established in the conventional $t$-$J$ chain, which we confirm here as a demonstration of the method. Turning on a multi-spin interaction $Q$ that eventually drives the system into a spontaneously dimerized (valence-bond solid, VBS) state, we can observe the features of spin-charge separation until the VBS transition takes place. While generally good agreement is found with the conventional analytical spin-charge separation ansatz, we point out the formation of a gap between two holon bands that in the ansatz are degenerate at $k=0$ and $k=\pi$. Inside the VBS phase, effectively attractive interactions may lead to the binding of the spinon and holon, of which we find evidence at large $Q\mathrm{/}J$. In the statically dimerized $t$-$J$ chain, we find equally spaced spin polaron bands corresponding to increasingly large bound states with two internal spin polaron modes – even and odd with respect to parton permutation. Our results overall demonstrate the power of modern analytic continuation tools in combination with large-scale QMC simulations.